In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka's formula for linear Brownian motion. The paper is closed with a description of the boundary process through the local times of the distances from the initial process to the facets.
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Nizar Demni, Dominique Lépingle, Brownian Motion, Reflection Groups and Tanaka Formula. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 41–55DOI 10.4171/RSMUP/127-3